Graph symmetry and dynamic systems

In this article efficient methods are developed for decomposing the graphs into subgraphs and healing the subgraphs to maintain the information corresponding to the eigenvalues and eigenvectors of the original graph for calculating the natural frequency of symmetric structures. Three canonical forms I, II and III are identified for the matrices involved, and applying graph theoretical concepts, symmetry is fully used in eigensolution of vibrating systems comprised of springs and masses.